Reaching as Cheap as Possible in 1-clock Robust Weighted Timed Games

2026-06-27

AI Summary

This study addresses the problem of determining the minimal cost for the Min player to achieve a reachability objective in single-clock robust weighted timed games, accounting for imprecise time measurements. Focusing on two-player zero-sum games equipped with a real-valued clock and integer weights, the work introduces a robust semantics to model temporal perturbations and leverages formal modeling, clock abstraction, and real-time system verification techniques for analysis. The primary contribution lies in establishing, for the first time, the decidability of the value problem for this class of games, thereby extending the boundary of known decidable subclasses and providing a theoretical foundation for synthesizing robust strategies in embedded and real-time systems.

Abstract

The value problem for 2-player games on graph generally consists in determining the minimal value Min can ensure against any possible strategy for Max. We consider here the value problem for reachability objectives in weighted timed games (WTGs) under a robust semantics. WTGs are a modelling formalism combining real-time constraints and integer weights on transitions and locations in an adversarial setting. Robustness allows for representing timing imprecisions in the measurement of delays and clock values. Robust weighted timed games have been introduced more than a decade ago: they are undecidable in general, and were quite recently shown decidable for the subclasses of acyclic or divergent robust WTGs. This paper pursues the goal of identifying decidable subclasses and establishes the decidability of the robust value problem for 1-clock WTGs.

Problem

• weighted timed games
• robust semantics
• reachability
• decidability
• 1-clock

Innovation

• robust weighted timed games
• decidability
• 1-clock
• value problem
• reachability